I think we differ on the meaning of rules. No shirt, no pants are behaviorial rules and not infringements on basic human rights. No shirt, no pants is hygenic in nature. No blacks - no guns are not behaviorial in my sense as while gun carrying is a behavior, it is more the instantiation of a basic human right.
Would a store be able to ban folks on NO crosses, no Yarmulkas? If they didn't pose some kind of physical risk, banning them would be religious discrimination. In the MRI, your cross would be a risk.
Thus, the property owner can forbid behaviorial aspects. I'm in favor of all guns must stay concealed in the store but the right to defend is fundamental.
While repeating myself, when you are open to the public - you can set behaviorial standards that do not violate human rights or for specific safety reasons. I don't believe you can set behavioral standards that violate rights if you decide that your store is not your private castle but a public space.
Similar arguments have been made about space in malls and airports. Organizations have argued that while private or government property, they have become the equivalent of the public square of old. Thus, folks could express themselves there if they did not engage in some obnoxious behavior. Thus, the precedent of extending rights to private places that become public in utilization is not unknown.
Now, this is too intellectual. How about will my 38 in a shoulder holster be sufficient when zombies attack the mall as I've seen in several movies. If I can't carry in the mall - who will stop the zombies?